This paper aims to develop a three-dimensional isogeometric-reproducing kernel particle method (IGA-RKPM) coupling approach to study the buckling behavior of cracked isotropic and orthotropic plate and shell structures. The IGA and RKPM-based meshfree methods are coupled successfully through a reproducing condition in the physical domain that guarantees the higher-order polynomial continuity of basis functions and overcomes the barrier of global parameterization in the physical domain. The resulting coupling approach not only preserves the geometry exactness and offers a higher-order approximation based on IGA basis functions but also allows local refinement flexibility. Linear eigenvalue buckling analyses for cracked orthotropic plate and shell structures have been carried out within the framework of the proposed coupling approach. The effects of several parameters such as the crack length ratio, thickness-to-length ratio, and orthotropy angle on the critical buckling stress of the structures have been investigated in detail under different boundary and loading conditions. The efficacy and robustness of the proposed coupling approach have been demonstrated by comparing the present results with those available in literature.

本文旨在发展一种三维等距重现核颗粒方法（IGA-RKPM）耦合方法，以研究破裂的各向同性和正交异性板壳结构的屈曲行为。基于IGA和RKPM的无网格方法通过物理域中的重现条件成功耦合，从而保证了基函数的高阶多项式连续性，并克服了物理域中全局参数化的障碍。最终的耦合方法不仅保留了几何精度，并且基于IGA基函数提供了更高阶的近似值，而且还提供了局部优化的灵活性。在所提出的耦合方法的框架内，已经对裂纹正交异性板和壳结构进行了线性特征值屈曲分析。在不同的边界和载荷条件下，详细研究了裂纹长度比，厚度长度比和正交各向异性角等几个参数对结构的临界屈曲应力的影响。通过将当前结果与文献中可获得的结果进行比较，已证明了所提出的耦合方法的有效性和鲁棒性。